Answer :
The formula for compounded interest is as follows:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A is the final amount, P is the principal amount (the initial amount), r is the annual interest rate, n is how many times it is compounded per year and t is the time in years.
We already have:
[tex]\begin{gathered} P=2000 \\ r=12\%=0.12 \\ t=6 \end{gathered}[/tex]Also, we know that it is compounded monthly. Since there are 12 month per year, each ear it will be compounded 12 times:
[tex]n=12[/tex]Now, to get the final amount, we just need to substitute this values and evaluate:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=2000(1+\frac{0.12}{12})^{12\cdot6} \\ A=2000(1+0.01)^{72} \\ A=2000(1.01)^{72} \\ A=2000\cdot2.0470\ldots \\ A=4094.1986\ldots\approx4094.20 \end{gathered}[/tex]So, the future value is approximately $4094.20.